Solve 10/x-4-2000/x^2-16

$$\frac { 10 } { x - 4 } - \frac { 2000 } { x ^ { 2 } - 16 }$$

Evaluate

$$\frac{10\left(x-196\right)}{x^{2}-16}$$

Short Solution Steps

Factor x^{2}-16.

$$\frac{10}{x-4}-\frac{2000}{\left(x-4\right)\left(x+4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+4\right) is \left(x-4\right)\left(x+4\right). Multiply \frac{10}{x-4} times \frac{x+4}{x+4}.

$$\frac{10\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{2000}{\left(x-4\right)\left(x+4\right)}$$

Since \frac{10\left(x+4\right)}{\left(x-4\right)\left(x+4\right)} and \frac{2000}{\left(x-4\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10\left(x+4\right)-2000}{\left(x-4\right)\left(x+4\right)}$$

Do the multiplications in 10\left(x+4\right)-2000.

$$\frac{10x+40-2000}{\left(x-4\right)\left(x+4\right)}$$

Combine like terms in 10x+40-2000.

$$\frac{10x-1960}{\left(x-4\right)\left(x+4\right)}$$

Expand \left(x-4\right)\left(x+4\right).

$$\frac{10x-1960}{x^{2}-16}$$

Factor

$$\frac{10\left(x-196\right)}{x^{2}-16}$$